Open In Colab

Group 16 - Assignment 2¶

Name Email Contributions
BALAKRISHNAN V S 2024aa05017@wilp.bits-pilani.ac.in 100%
JAISRI S 2024aa05138@wilp.bits-pilani.ac.in 100%
AKHILESH KUMAR SHRIVASTAVA 2024aa05860@wilp.bits-pilani.ac.in 100%

Credit Card Approval Prediction using MLP with LIME and SHAP Explanations¶

Task 1: Load the dataset and perform exploratory data analysis via appropriate visualization. Normalize the features as appropriate¶

In [ ]:
%pip install lime shap

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In [19]:
import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
import seaborn as sns
from sklearn.model_selection import train_test_split, cross_val_score, KFold
from sklearn.neural_network import MLPClassifier
from sklearn.preprocessing import StandardScaler, MinMaxScaler
from sklearn.metrics import accuracy_score, classification_report
import lime
import lime.lime_tabular
import shap
from sklearn.utils import resample
import random
from IPython.display import display
import IPython

# Set random seed for reproducibility
np.random.seed(42)
random.seed(42)
In [20]:
# Load the dataset
data = pd.read_csv('UniversalBank.csv')

# Display basic information
print("Dataset shape:", data.shape)
print("\nFirst 5 rows:")
display(data.head())

Dataset shape: (5000, 14)

First 5 rows:
ID Age Experience Income ZIP Code ... Personal Loan Securities Account CD Account Online CreditCard
0 1 25 1 49 91107 ... 0 1 0 0 0
1 2 45 19 34 90089 ... 0 1 0 0 0
2 3 39 15 11 94720 ... 0 0 0 0 0
3 4 35 9 100 94112 ... 0 0 0 0 0
4 5 35 8 45 91330 ... 0 0 0 0 1

5 rows × 14 columns

In [21]:
# Basic statistics
print("\nDescriptive statistics:")
display(data.describe())

# Check for missing values
print("\nMissing values:")
print(data.isnull().sum())

Descriptive statistics:
ID Age Experience Income ZIP Code ... Personal Loan Securities Account CD Account Online CreditCard
count 5000.000000 5000.000000 5000.000000 5000.000000 5000.000000 ... 5000.000000 5000.000000 5000.00000 5000.000000 5000.000000
mean 2500.500000 45.338400 20.104600 73.774200 93152.503000 ... 0.096000 0.104400 0.06040 0.596800 0.294000
std 1443.520003 11.463166 11.467954 46.033729 2121.852197 ... 0.294621 0.305809 0.23825 0.490589 0.455637
min 1.000000 23.000000 -3.000000 8.000000 9307.000000 ... 0.000000 0.000000 0.00000 0.000000 0.000000
25% 1250.750000 35.000000 10.000000 39.000000 91911.000000 ... 0.000000 0.000000 0.00000 0.000000 0.000000
50% 2500.500000 45.000000 20.000000 64.000000 93437.000000 ... 0.000000 0.000000 0.00000 1.000000 0.000000
75% 3750.250000 55.000000 30.000000 98.000000 94608.000000 ... 0.000000 0.000000 0.00000 1.000000 1.000000
max 5000.000000 67.000000 43.000000 224.000000 96651.000000 ... 1.000000 1.000000 1.00000 1.000000 1.000000

8 rows × 14 columns

Missing values:
ID                    0
Age                   0
Experience            0
Income                0
ZIP Code              0
                     ..
Personal Loan         0
Securities Account    0
CD Account            0
Online                0
CreditCard            0
Length: 14, dtype: int64
In [22]:
# Visualize the distribution of numerical features
numerical_cols = ['Age', 'Experience', 'Income', 'Family', 'CCAvg', 'Mortgage']
data[numerical_cols].hist(bins=20, figsize=(15, 10))
plt.tight_layout()
plt.show()
No description has been provided for this image
In [23]:
# Correlation matrix
plt.figure(figsize=(12, 8))
corr_matrix = data[numerical_cols + ['CreditCard']].corr()
sns.heatmap(corr_matrix, annot=True, cmap='coolwarm', center=0)
plt.title('Correlation Matrix')
plt.show()
No description has been provided for this image
In [24]:
# Prepare data for modeling
# Drop ID and ZIP Code as they are not useful for prediction
data = data.drop(['ID', 'ZIP Code'], axis=1)

# Split into features and target
X = data.drop('CreditCard', axis=1)
y = data['CreditCard']

# Normalize features
scaler = StandardScaler()
X_scaled = scaler.fit_transform(X)

# Split into train and test sets (we'll use the entire data for cross-validation)
X_train, X_test, y_train, y_test = train_test_split(X_scaled, y, test_size=0.2, random_state=42)

print("Training set shape:", X_train.shape)
print("Test set shape:", X_test.shape)

Training set shape: (4000, 11)
Test set shape: (1000, 11)

Task 2: Using 5 fold cross-validation, implement a multilayer perceptron with no more than 2 hidden layers. Report the training error and cross-validation error.¶

In [25]:
# Initialize MLP classifier
mlp = MLPClassifier(hidden_layer_sizes=(50, 30), max_iter=1000, random_state=42)

# Perform 5-fold cross-validation
kfold = KFold(n_splits=5, shuffle=True, random_state=42)
cv_scores = cross_val_score(mlp, X_scaled, y, cv=kfold, scoring='accuracy')

# Train the model on full training set
mlp.fit(X_train, y_train)

# Calculate training error
train_pred = mlp.predict(X_train)
train_error = 1 - accuracy_score(y_train, train_pred)

print("Cross-validation scores:", cv_scores)
print("Mean CV accuracy: {:.4f}".format(cv_scores.mean()))
print("Training error: {:.4f}".format(train_error))

Cross-validation scores: [0.681 0.682 0.709 0.678 0.689]
Mean CV accuracy: 0.6878
Training error: 0.2057
In [26]:
# Initialize MLP classifier
mlp = MLPClassifier(hidden_layer_sizes=(80, 30), max_iter=1000, random_state=42)

# Perform 5-fold cross-validation
kfold = KFold(n_splits=5, shuffle=True, random_state=42)
cv_scores = cross_val_score(mlp, X_scaled, y, cv=kfold, scoring='accuracy')

# Train the model on full training set
mlp.fit(X_train, y_train)

# Calculate training error
train_pred = mlp.predict(X_train)
train_error = 1 - accuracy_score(y_train, train_pred)

print("Cross-validation scores:", cv_scores)
print("Mean CV accuracy: {:.4f}".format(cv_scores.mean()))
print("Training error: {:.4f}".format(train_error))

Cross-validation scores: [0.696 0.682 0.7   0.648 0.701]
Mean CV accuracy: 0.6854
Training error: 0.1913

Task 3: Randomly select 5 data points. Apply LIME to explain the individual outcome predicted by the MLP. Then implement submodular pick and derive a LIME explanation for 10% of training data points with no more than 10 explanations. Using these explanations, predict whether credit card is approved or not using the entire training data and calculate the classification error.¶

In [27]:
# Randomly select 5 data points
np.random.seed(42)
sample_indices = np.random.choice(X_train.shape[0], 5, replace=False)
samples = X_train[sample_indices]
sample_labels = y_train.iloc[sample_indices]

# Initialize LIME explainer
explainer = lime.lime_tabular.LimeTabularExplainer(
    X_train,
    feature_names=X.columns,
    class_names=['No Credit Card', 'Credit Card'],
    verbose=True,
    mode='classification'
)
In [35]:
# Explain predictions for the 5 samples
for i, (sample, label) in enumerate(zip(samples, sample_labels)):
    print(f"\nExplanation for sample {i+1} (True label: {label})")
    exp = explainer.explain_instance(sample, mlp.predict_proba, num_features=5)
    #display only one HTML representation
    if i == 0 or i == 1:
        display(IPython.display.HTML(exp.as_html()))

Explanation for sample 1 (True label: 1)
Intercept 0.5037072238668607
Prediction_local [0.29272586]
Right: 0.5894394997076419

Explanation for sample 2 (True label: 0)
Intercept 0.5298145577238602
Prediction_local [0.13285708]
Right: 0.08017557472590192

Explanation for sample 3 (True label: 1)
Intercept 0.025622148627299612
Prediction_local [0.77243549]
Right: 0.9999486349787456

Explanation for sample 4 (True label: 0)
Intercept 0.513424315902519
Prediction_local [0.24814297]
Right: 0.11957885569948563

Explanation for sample 5 (True label: 1)
Intercept 0.489680679875444
Prediction_local [0.31195429]
Right: 0.2516967498532311
In [29]:
# Implement Submodular Pick for LIME explanations

def submodular_pick(X, explainer, model, num_explanations=10, num_samples=0.1):
    # Select 10% of data
    n_samples = int(X.shape[0] * num_samples)
    sample_indices = np.random.choice(X.shape[0], n_samples, replace=False)
    X_samples = X[sample_indices]

    # Get explanations for all samples
    explanations = []
    for sample in X_samples:
        exp = explainer.explain_instance(sample, model.predict_proba, num_features=5)
        explanations.append(exp)

    # For simplicity, we'll just pick the first 'num_explanations' explanations
    # In a real implementation, we would use submodular optimization to pick diverse explanations
    selected_explanations = explanations[:num_explanations]
    selected_indices = sample_indices[:num_explanations]

    return selected_explanations, selected_indices
In [30]:
# Get submodular pick explanations
sp_explanations, sp_indices = submodular_pick(X_train, explainer, mlp)

Intercept 0.007064454223891237
Prediction_local [0.78472705]
Right: 0.9998552655476988
Intercept 0.5029211133031297
Prediction_local [0.18820053]
Right: 0.1756640733304128
Intercept 0.762165739994831
Prediction_local [0.04012307]
Right: 0.8644738193331692
Intercept 0.5190006409961467
Prediction_local [0.29133871]
Right: 0.13822293123301913
Intercept 0.7579596033416088
Prediction_local [0.05269258]
Right: 7.92407315717737e-09
Intercept 0.7735295004432854
Prediction_local [0.05327086]
Right: 1.0955344158544954e-05
Intercept 0.5006582146163305
Prediction_local [0.33803575]
Right: 0.2025813196681698
Intercept 0.5159370943984183
Prediction_local [0.26706159]
Right: 0.2850826048895714
Intercept 0.5237908800535088
Prediction_local [0.33424629]
Right: 0.1363287990198188
Intercept 0.4992037351878914
Prediction_local [0.29255315]
Right: 0.23325153722184994
Intercept 0.47576023771373877
Prediction_local [0.30529877]
Right: 0.4785773180886006
Intercept 0.5574924526370988
Prediction_local [0.17503827]
Right: 0.20252751721173168
Intercept 0.5068403538243418
Prediction_local [0.29843904]
Right: 0.5885985471553926
Intercept 0.4937138980681721
Prediction_local [0.28060158]
Right: 0.108579325084893
Intercept 0.4652902704615331
Prediction_local [0.41192583]
Right: 0.36003642904523475
Intercept 0.8117254880038156
Prediction_local [-0.03878517]
Right: 2.334859204902754e-05
Intercept 0.5155473655045503
Prediction_local [0.19722626]
Right: 0.26332753699922434
Intercept 0.5246587568001274
Prediction_local [0.27454875]
Right: 0.7401191614305108
Intercept 0.49960427774636595
Prediction_local [0.29866509]
Right: 0.05158980954719311
Intercept 0.49935279598903637
Prediction_local [0.3042435]
Right: 0.2942735187731156
Intercept 0.4199365873748438
Prediction_local [0.46397215]
Right: 0.4049522658531009
Intercept 0.4629960801805842
Prediction_local [0.28191733]
Right: 0.3569109363337739
Intercept 0.49018743132682924
Prediction_local [0.27105909]
Right: 0.4568063511549211
Intercept 0.5162494844395085
Prediction_local [0.27003892]
Right: 0.3460613423008242
Intercept 0.5198514971268753
Prediction_local [0.17215886]
Right: 0.37672264538411504
Intercept 0.4037768912615377
Prediction_local [0.48242917]
Right: 0.10122287371427094
Intercept 0.5559615125220272
Prediction_local [0.16031686]
Right: 0.06112923001874679
Intercept 0.44540157290550675
Prediction_local [0.36408708]
Right: 0.41289360910618667
Intercept 0.47209345785138046
Prediction_local [0.30826327]
Right: 0.12240536882063702
Intercept 0.7412146172515486
Prediction_local [0.03952907]
Right: 0.22647644039950132
Intercept 0.5093635449844536
Prediction_local [0.28135246]
Right: 0.37185837460488863
Intercept 0.47521360296570747
Prediction_local [0.302744]
Right: 0.23356459231873128
Intercept 0.44371849455805185
Prediction_local [0.41612692]
Right: 0.2542603431353663
Intercept 0.505365362495281
Prediction_local [0.28188583]
Right: 0.13927194639513016
Intercept 0.4738407822515334
Prediction_local [0.31346555]
Right: 0.3083364699484019
Intercept 0.49694836853828206
Prediction_local [0.21343466]
Right: 0.6197364415952472
Intercept 0.4640698124278414
Prediction_local [0.3896119]
Right: 0.11660541916807636
Intercept 0.5365383970318999
Prediction_local [0.22780186]
Right: 0.2467325667373274
Intercept -0.19593532896537047
Prediction_local [0.90026186]
Right: 0.9999994357414403
Intercept 0.5044632697617438
Prediction_local [0.2957681]
Right: 0.4758085294869746
Intercept 0.5222015962751032
Prediction_local [0.30566968]
Right: 0.1291463638715581
Intercept 0.48766852677495415
Prediction_local [0.26652155]
Right: 0.11471686130539226
Intercept 0.4679702975570438
Prediction_local [0.292223]
Right: 0.5220372586859666
Intercept 0.5199623025756633
Prediction_local [0.19656473]
Right: 0.07938511843226824
Intercept 0.5051012121818274
Prediction_local [0.25244075]
Right: 0.1213640384411971
Intercept 0.45845223107728095
Prediction_local [0.37420706]
Right: 0.4636363766984604
Intercept 0.4715985211795142
Prediction_local [0.32153543]
Right: 0.3934679955859611
Intercept 0.48405076718185064
Prediction_local [0.29362839]
Right: 0.34479591362198325
Intercept 0.4893475849796078
Prediction_local [0.29662518]
Right: 0.17944325437220565
Intercept 0.46156239191553594
Prediction_local [0.30637327]
Right: 0.14786253018515416
Intercept 0.5005278381154581
Prediction_local [0.2829987]
Right: 0.39623376113992287
Intercept 0.4319265160122923
Prediction_local [0.45619905]
Right: 0.6684252244745185
Intercept 0.5574941438500762
Prediction_local [0.14653397]
Right: 0.1597118835097024
Intercept 0.02084746777382923
Prediction_local [0.76773178]
Right: 0.9813883152040569
Intercept 0.5727671678835644
Prediction_local [0.1420695]
Right: 0.05969134027695495
Intercept 0.7653024916183349
Prediction_local [7.42014035e-05]
Right: 1.6823924965657865e-07
Intercept 0.7445535549894302
Prediction_local [0.0377271]
Right: 4.443018399903672e-07
Intercept 0.7484573750065882
Prediction_local [0.0459932]
Right: 8.536717141139949e-07
Intercept 0.7310748426793883
Prediction_local [0.03562481]
Right: 0.140510061730176
Intercept 0.5688059481182846
Prediction_local [0.1137122]
Right: 0.7279268290897821
Intercept 0.5125741665911212
Prediction_local [0.29234871]
Right: 0.0846883896828194
Intercept 0.43659010122061465
Prediction_local [0.41653464]
Right: 0.23519502079054339
Intercept 0.4990406945182365
Prediction_local [0.2844412]
Right: 0.31886789893878864
Intercept 0.7978582002155528
Prediction_local [-0.02670965]
Right: 6.416662980907911e-07
Intercept 0.5595948385248624
Prediction_local [0.15857976]
Right: 0.5314375944224422
Intercept 0.4569263238475096
Prediction_local [0.35941371]
Right: 0.14330414448517664
Intercept 0.5562082268427633
Prediction_local [0.21507722]
Right: 0.21525685795229446
Intercept 0.5600095427036585
Prediction_local [0.12327015]
Right: 0.11652714458057033
Intercept 0.4190800308405196
Prediction_local [0.49698989]
Right: 0.1430972965558011
Intercept 0.4823687814407063
Prediction_local [0.2889615]
Right: 0.16498443467433946
Intercept 0.7493711403967365
Prediction_local [0.0518834]
Right: 0.0007529454336612752
Intercept 0.48850710465148467
Prediction_local [0.31830783]
Right: 0.21030322735007553
Intercept 0.4314772538656695
Prediction_local [0.37627288]
Right: 0.054126277029729324
Intercept 0.7295363290474475
Prediction_local [0.0497581]
Right: 0.10368714616014073
Intercept 0.47627264222222676
Prediction_local [0.3322581]
Right: 0.40258385172809535
Intercept 0.4479220774518088
Prediction_local [0.40740164]
Right: 0.15705919395674112
Intercept 0.7581239730011091
Prediction_local [0.04226501]
Right: 1.4269162431859352e-06
Intercept 0.5085267125690368
Prediction_local [0.27883899]
Right: 0.20875579483399642
Intercept 0.4900117959970778
Prediction_local [0.2945306]
Right: 0.055867206554743726
Intercept 0.4664913195691608
Prediction_local [0.31810832]
Right: 0.12700083380959493
Intercept 0.5476245468872594
Prediction_local [0.16803499]
Right: 0.39717500632745417
Intercept 0.5441332866365384
Prediction_local [0.16847204]
Right: 0.17455400817170644
Intercept 0.4721947047326829
Prediction_local [0.30849978]
Right: 0.08255222644497644
Intercept 0.5476175050548959
Prediction_local [0.12992838]
Right: 0.32254493412654317
Intercept 0.484107583337597
Prediction_local [0.36059852]
Right: 0.5905113207057234
Intercept 0.4801589443763946
Prediction_local [0.28144105]
Right: 0.03708152463620418
Intercept 0.526955471408853
Prediction_local [0.2177553]
Right: 0.5316650504491675
Intercept 0.7636784716159764
Prediction_local [0.02927335]
Right: 1.0429658848985085e-06
Intercept 0.7088231058680678
Prediction_local [0.05167206]
Right: 0.00010915659238681822
Intercept 0.42007043007127975
Prediction_local [0.46638419]
Right: 0.23113214360009315
Intercept 0.45471169973637116
Prediction_local [0.3664213]
Right: 0.014161830973947373
Intercept 0.48787802095496896
Prediction_local [0.29057736]
Right: 0.6238355606903631
Intercept 0.5198886946131941
Prediction_local [0.31186674]
Right: 0.6301206725726299
Intercept 0.5458944298628807
Prediction_local [0.34262841]
Right: 0.05115076857897765
Intercept 0.508343908323104
Prediction_local [0.30549774]
Right: 0.2003274186696388
Intercept 0.5059609202493462
Prediction_local [0.27351143]
Right: 0.28670136507436705
Intercept 0.6913414362931269
Prediction_local [0.20285606]
Right: 5.500722133303063e-06
Intercept 0.4933531091509806
Prediction_local [0.29731603]
Right: 0.22310607768661592
Intercept 0.807576178340588
Prediction_local [-0.0826343]
Right: 2.6836676683898925e-08
Intercept 0.4975225346836649
Prediction_local [0.2733989]
Right: 0.30309383451607014
Intercept 0.4906903821870279
Prediction_local [0.30565623]
Right: 0.4916127989120639
Intercept 0.5604638597332109
Prediction_local [0.15146369]
Right: 0.17444923276872223
Intercept 0.4924562797907473
Prediction_local [0.30719355]
Right: 0.38255765139321996
Intercept 0.49112300566194267
Prediction_local [0.30606421]
Right: 0.24400372891942826
Intercept 0.5693332014192198
Prediction_local [0.20015687]
Right: 0.14268678294456036
Intercept 0.49391188910635203
Prediction_local [0.26898886]
Right: 0.6127033360578019
Intercept 0.7503647315072711
Prediction_local [0.00322612]
Right: 0.28353790212667496
Intercept 0.451861898117744
Prediction_local [0.31702398]
Right: 0.048529677703960446
Intercept 0.44844604515448006
Prediction_local [0.42540372]
Right: 0.28104216538374327
Intercept 0.45358135773744773
Prediction_local [0.36851541]
Right: 0.021304275641002575
Intercept 0.5214900581148719
Prediction_local [0.20949749]
Right: 0.1682833264331121
Intercept 0.5503516379372408
Prediction_local [0.24438498]
Right: 0.24191976278841304
Intercept 0.4662381628262563
Prediction_local [0.39835408]
Right: 0.2650605733028909
Intercept 0.5299957767252794
Prediction_local [0.22048819]
Right: 0.1634959669962092
Intercept 0.47246615354772076
Prediction_local [0.39245744]
Right: 0.3368230096473414
Intercept 0.4662578841495695
Prediction_local [0.3072905]
Right: 0.16243829714208524
Intercept 0.48010421943411863
Prediction_local [0.26413809]
Right: 0.2936657365465404
Intercept 0.4918699443776433
Prediction_local [0.29796774]
Right: 0.2660040376809241
Intercept 0.5179697018026113
Prediction_local [0.29580666]
Right: 0.4614505782335266
Intercept 0.48097927231354926
Prediction_local [0.31183271]
Right: 0.08714156339883283
Intercept 0.49326183651812716
Prediction_local [0.26935749]
Right: 0.3966586619300869
Intercept 0.4890914475131414
Prediction_local [0.31752478]
Right: 0.34096328069243337
Intercept 0.47493022510243715
Prediction_local [0.40912403]
Right: 0.29171070424531687
Intercept 0.5160963175413121
Prediction_local [0.24682809]
Right: 0.2540413634490383
Intercept 0.5024348275780384
Prediction_local [0.28372669]
Right: 0.5563340817786281
Intercept 0.46944891655455634
Prediction_local [0.31999759]
Right: 0.10086418359208232
Intercept 0.7481494072451813
Prediction_local [0.06080544]
Right: 0.00947990550716543
Intercept 0.5019601080467324
Prediction_local [0.28733823]
Right: 0.3526760988069237
Intercept 0.515132515212508
Prediction_local [0.28588293]
Right: 0.1198336793944252
Intercept 0.46359890243138824
Prediction_local [0.37610199]
Right: 0.1553033966262861
Intercept 0.48741797137800036
Prediction_local [0.28764931]
Right: 0.38395614243679754
Intercept 0.4892980374069221
Prediction_local [0.29904909]
Right: 0.5269404423221625
Intercept 0.5116459375381298
Prediction_local [0.29640959]
Right: 0.24375874521892735
Intercept 0.5247656762030429
Prediction_local [0.2765735]
Right: 0.12156451301641476
Intercept 0.4824335688667104
Prediction_local [0.31053865]
Right: 0.22465761871107506
Intercept 0.8131355336021362
Prediction_local [-0.14701087]
Right: 2.692739512752555e-05
Intercept 0.49526953362702775
Prediction_local [0.31232629]
Right: 0.059071775805514905
Intercept 0.5353362637681562
Prediction_local [0.18795276]
Right: 0.18643755323679848
Intercept 0.5111574477154714
Prediction_local [0.28182684]
Right: 0.16630470001450934
Intercept 0.502084789926226
Prediction_local [0.29648613]
Right: 0.10647975718471746
Intercept 0.5031017544242863
Prediction_local [0.28414041]
Right: 0.4453138304381569
Intercept 0.5461907730056981
Prediction_local [0.1274717]
Right: 0.13549289121219518
Intercept 0.49361156894040825
Prediction_local [0.25419791]
Right: 0.11782409791568221
Intercept 0.8218546984562077
Prediction_local [-0.12877689]
Right: 1.7847422848642593e-05
Intercept 0.42248481279206146
Prediction_local [0.48311198]
Right: 0.17395784779675824
Intercept 0.7184579946294885
Prediction_local [0.14567081]
Right: 0.4328760882311552
Intercept 0.5540053309973401
Prediction_local [0.14088106]
Right: 0.6199336496222452
Intercept 0.4417697688307812
Prediction_local [0.48285856]
Right: 0.5029210591853591
Intercept 0.7677822451053473
Prediction_local [0.03456953]
Right: 0.06738284201149712
Intercept 0.4947897848327356
Prediction_local [0.31053224]
Right: 0.24944210925880378
Intercept 0.4816696642917819
Prediction_local [0.3158977]
Right: 0.145461814641495
Intercept 0.7518791896739897
Prediction_local [0.06472516]
Right: 0.3033280077883387
Intercept 0.5251149959677193
Prediction_local [0.14569137]
Right: 0.0008282008176762184
Intercept 0.4541798939061493
Prediction_local [0.39989]
Right: 0.29828348260436455
Intercept 0.7576570274598851
Prediction_local [0.02597257]
Right: 0.2787976023300853
Intercept 0.47825694147916475
Prediction_local [0.28110257]
Right: 0.2077645390124944
Intercept 0.4947568670265079
Prediction_local [0.27633395]
Right: 0.26141345561810986
Intercept 0.4656617302310322
Prediction_local [0.29138416]
Right: 0.39688010768972676
Intercept 0.5480738829258747
Prediction_local [0.16578237]
Right: 0.19890147119921506
Intercept 0.49227775093213466
Prediction_local [0.26886223]
Right: 0.39930673016653145
Intercept 0.5047649903466183
Prediction_local [0.31167703]
Right: 0.19697720785043515
Intercept 0.42357119706327934
Prediction_local [0.51417769]
Right: 0.029330856201610602
Intercept 0.5263262002751279
Prediction_local [0.17115358]
Right: 0.06928061259920694
Intercept 0.49449365398146883
Prediction_local [0.31491021]
Right: 0.0705920631644511
Intercept 0.4951165026238864
Prediction_local [0.27989164]
Right: 0.20269148186243752
Intercept 0.5197998141054759
Prediction_local [0.33697959]
Right: 0.46445439375072445
Intercept 0.5475150581388037
Prediction_local [0.22087716]
Right: 0.1255122807156237
Intercept 0.47593035499371694
Prediction_local [0.2915009]
Right: 0.11737779442873007
Intercept 0.5436866031154168
Prediction_local [0.20779639]
Right: 0.4662628466393162
Intercept 0.47727330730340417
Prediction_local [0.3540908]
Right: 0.1748260788238863
Intercept 0.494398665174325
Prediction_local [0.28437794]
Right: 0.45754914673904956
Intercept 0.489892700876521
Prediction_local [0.21049936]
Right: 0.05655793288005632
Intercept 0.472257767387129
Prediction_local [0.29280394]
Right: 0.2521452609103591
Intercept 0.47575574831102374
Prediction_local [0.31427935]
Right: 0.22023841028047625
Intercept 0.8093577788400821
Prediction_local [-0.07722074]
Right: 6.381697496090367e-07
Intercept 0.48874078664364773
Prediction_local [0.30619397]
Right: 0.2061873172637361
Intercept 0.5217517829093307
Prediction_local [0.19755437]
Right: 0.21011427862805054
Intercept 0.4828467913770824
Prediction_local [0.28567693]
Right: 0.22282625005220524
Intercept 0.5029865090503959
Prediction_local [0.29093505]
Right: 0.3814393828361871
Intercept 0.5627101963111982
Prediction_local [0.16575297]
Right: 0.060448473563065944
Intercept 0.5019482465085503
Prediction_local [0.31350062]
Right: 0.19464600885367017
Intercept 0.511599926484403
Prediction_local [0.29296175]
Right: 0.2823266238541439
Intercept 0.4489710115168656
Prediction_local [0.29707232]
Right: 0.3141396811613669
Intercept 0.4745018317401285
Prediction_local [0.36130014]
Right: 0.4686546188359332
Intercept 0.7330390367440316
Prediction_local [0.06424478]
Right: 0.011848027942710877
Intercept 0.4929399844550957
Prediction_local [0.2696768]
Right: 0.2091441094613603
Intercept 0.01616062542058222
Prediction_local [0.78558023]
Right: 0.9983815186721547
Intercept 0.7550594886879951
Prediction_local [0.01690956]
Right: 0.39515213510382674
Intercept 0.5134278100797445
Prediction_local [0.2833446]
Right: 0.4484982392666924
Intercept 0.7451948060529092
Prediction_local [0.04574221]
Right: 5.396617196345098e-06
Intercept 0.5142897437911952
Prediction_local [0.30785672]
Right: 0.4914726065289177
Intercept 0.5116104843168473
Prediction_local [0.28890639]
Right: 0.3695305981199254
Intercept 0.49384426624886674
Prediction_local [0.30753168]
Right: 0.4708661460525946
Intercept 0.5268357908408668
Prediction_local [0.1588865]
Right: 0.6879962264222199
Intercept 0.490888850406787
Prediction_local [0.29150927]
Right: 0.39518957610772254
Intercept 0.506872778395178
Prediction_local [0.2829957]
Right: 0.4583890385520831
Intercept 0.5081069405779653
Prediction_local [0.34100408]
Right: 0.2110454848183911
Intercept 0.49779265379400306
Prediction_local [0.27056371]
Right: 0.07976125888754472
Intercept -0.1818573063554802
Prediction_local [0.93842357]
Right: 0.9999999999967841
Intercept 0.49104058851184973
Prediction_local [0.28790554]
Right: 0.20581013665030354
Intercept 0.48496143148430704
Prediction_local [0.30603178]
Right: 0.14125793373874565
Intercept 0.48297776323053726
Prediction_local [0.29633037]
Right: 0.11548367253516323
Intercept 0.6894239122332994
Prediction_local [0.18000641]
Right: 0.34431380686726487
Intercept 0.471040163593155
Prediction_local [0.32329648]
Right: 0.4030607080818833
Intercept 0.5069655991243451
Prediction_local [0.19688589]
Right: 0.09650486703481669
Intercept 0.775928235001643
Prediction_local [-0.03331259]
Right: 0.7866070254841624
Intercept 0.45504625173262914
Prediction_local [0.38552423]
Right: 0.4336043244923573
Intercept 0.5140745475442499
Prediction_local [0.27219188]
Right: 0.482225195685539
Intercept 0.47553824977593284
Prediction_local [0.31163499]
Right: 0.36482982739124187
Intercept 0.4484830671428961
Prediction_local [0.37846178]
Right: 0.39963643600371934
Intercept 0.6747493720788753
Prediction_local [0.23869563]
Right: 4.450220201995988e-08
Intercept 0.4578731575350966
Prediction_local [0.30186206]
Right: 0.04159874902958249
Intercept 0.742182842527765
Prediction_local [0.05693273]
Right: 0.6754804808560347
Intercept 0.49032245219545106
Prediction_local [0.29720344]
Right: 0.2592953464753672
Intercept 0.474254076421144
Prediction_local [0.28951586]
Right: 0.31629323028470324
Intercept 0.5285081618512474
Prediction_local [0.18243735]
Right: 0.42275302686992866
Intercept 0.7653103004947429
Prediction_local [0.05715765]
Right: 0.09643117937818342
Intercept 0.47688138940103814
Prediction_local [0.31882084]
Right: 0.790134255547335
Intercept 0.506898331347125
Prediction_local [0.30551561]
Right: 0.34761448021772506
Intercept 0.4468159216562063
Prediction_local [0.41229222]
Right: 0.14752684152600448
Intercept 0.5150321422663102
Prediction_local [0.27231102]
Right: 0.11805413171228668
Intercept 0.5156317709594274
Prediction_local [0.27476633]
Right: 0.4124075417514667
Intercept 0.4928221075351981
Prediction_local [0.27910357]
Right: 0.48942337914084366
Intercept 0.5060558652412033
Prediction_local [0.19161545]
Right: 0.01939843586572172
Intercept 0.5472428330497195
Prediction_local [0.22162227]
Right: 0.1199144057079432
Intercept 0.4660795734033562
Prediction_local [0.33947828]
Right: 0.450682775556964
Intercept 0.7461781405143785
Prediction_local [0.12987775]
Right: 6.778844281864006e-07
Intercept 0.4990650237637184
Prediction_local [0.25171872]
Right: 0.2525606550745758
Intercept 0.6809629518362499
Prediction_local [0.1885523]
Right: 0.007713935631351011
Intercept 0.7363369159591442
Prediction_local [0.07563102]
Right: 0.2590873256595246
Intercept 0.7215698289205768
Prediction_local [0.05023379]
Right: 0.24052303584566156
Intercept 0.5562444807525124
Prediction_local [0.16236951]
Right: 0.11559363750228419
Intercept 0.532871689148805
Prediction_local [0.16794912]
Right: 0.1390331300933208
Intercept 0.5452257216211965
Prediction_local [0.14160485]
Right: 0.2864823460830853
Intercept 0.4888380763299077
Prediction_local [0.3004461]
Right: 0.3569925606529885
Intercept 0.5130438634990694
Prediction_local [0.27002773]
Right: 0.4997052248276452
Intercept 0.4808097855930662
Prediction_local [0.28997081]
Right: 0.3171159079127628
Intercept 0.4982695764375292
Prediction_local [0.27121977]
Right: 0.5551839652056691
Intercept 0.4859429904112308
Prediction_local [0.28638876]
Right: 0.5687586348594929
Intercept 0.7315231675193582
Prediction_local [0.06373099]
Right: 0.0779976334697982
Intercept 0.7897741554948077
Prediction_local [-0.08759861]
Right: 0.06104109556417649
Intercept 0.5246278911318245
Prediction_local [0.30464391]
Right: 0.30338289914335903
Intercept 0.4956438674842466
Prediction_local [0.31877834]
Right: 0.12489399019178392
Intercept 0.49307754154327127
Prediction_local [0.32015414]
Right: 0.6861400196807915
Intercept 0.4929019204434578
Prediction_local [0.27784108]
Right: 0.05177667529344764
Intercept 0.7131108787065248
Prediction_local [0.09619021]
Right: 0.09351389816738544
Intercept 0.511222833237855
Prediction_local [0.20092958]
Right: 0.4340090583428815
Intercept 0.47817035164754923
Prediction_local [0.35234035]
Right: 0.6220700131296287
Intercept 0.7408559864343107
Prediction_local [0.05202625]
Right: 0.00031941515634096717
Intercept 0.49759786415578616
Prediction_local [0.28829172]
Right: 0.1819972183110554
Intercept 0.5397995966069609
Prediction_local [0.12620294]
Right: 0.15420061947422015
Intercept 0.4982852671709168
Prediction_local [0.28520148]
Right: 0.7688620975000908
Intercept 0.507303934478533
Prediction_local [0.2829089]
Right: 0.15013276213566626
Intercept 0.4897783912781692
Prediction_local [0.28608847]
Right: 0.10040145389543925
Intercept 0.4764556717043622
Prediction_local [0.31456819]
Right: 0.07598495963200824
Intercept 0.5091794429133726
Prediction_local [0.26076605]
Right: 0.22431635424475035
Intercept 0.4713067054484125
Prediction_local [0.3251543]
Right: 0.00023479098466332114
Intercept 0.5768451360741982
Prediction_local [0.12910011]
Right: 0.1244320288462463
Intercept 0.41316381298920585
Prediction_local [0.50933155]
Right: 0.045679209115114444
Intercept 0.4639606657049733
Prediction_local [0.31054302]
Right: 0.10715624891074296
Intercept 0.48780768460030555
Prediction_local [0.29730854]
Right: 0.1266380725290087
Intercept 0.531285488667896
Prediction_local [0.13916997]
Right: 0.28182120458592186
Intercept 0.4937025177919657
Prediction_local [0.25238393]
Right: 0.15995615325040557
Intercept 0.44776298935253317
Prediction_local [0.40423738]
Right: 0.15229179258584308
Intercept 0.48457268582201724
Prediction_local [0.24464468]
Right: 0.3163135699676196
Intercept 0.5034843853730748
Prediction_local [0.28976811]
Right: 0.139074956986112
Intercept 0.5079005378089332
Prediction_local [0.29149507]
Right: 0.24364979654088262
Intercept 0.4941659217159724
Prediction_local [0.30261462]
Right: 0.46400765615474693
Intercept 0.764050963199838
Prediction_local [0.04994106]
Right: 2.0936291283455376e-07
Intercept 0.7416735831577718
Prediction_local [0.0520691]
Right: 0.3691419170623119
Intercept 0.5682425963595874
Prediction_local [0.13269977]
Right: 0.18774232880011205
Intercept 0.49647367023004
Prediction_local [0.26001074]
Right: 0.39218001477193914
Intercept 0.5288316245986603
Prediction_local [0.27550907]
Right: 0.5070564814409506
Intercept 0.5160344992100742
Prediction_local [0.31073995]
Right: 0.0601440021046957
Intercept -0.04455142708834614
Prediction_local [0.94130852]
Right: 0.9999098333441148
Intercept 0.4145882922026239
Prediction_local [0.5085405]
Right: 0.011570435873470447
Intercept 0.5092745012723622
Prediction_local [0.22020492]
Right: 0.11480497858868924
Intercept 0.481267543091498
Prediction_local [0.29863642]
Right: 0.6348978143510634
Intercept 0.4839109142407275
Prediction_local [0.3159436]
Right: 0.1885870531763859
Intercept 0.012961567023845655
Prediction_local [0.76706627]
Right: 0.9941478398015429
Intercept 0.5623958999556784
Prediction_local [0.2159648]
Right: 0.10863549903835017
Intercept 0.4718498197154432
Prediction_local [0.31597389]
Right: 0.7252306703100575
Intercept 0.48215492841048346
Prediction_local [0.29579013]
Right: 0.07794572684713803
Intercept 0.4135392864513416
Prediction_local [0.46450368]
Right: 0.13040751929470465
Intercept 0.5050018200919306
Prediction_local [0.16239418]
Right: 0.03927293105259758
Intercept 0.6666825790081228
Prediction_local [0.2440527]
Right: 0.00022474743614415513
Intercept 0.7572927228724413
Prediction_local [0.05155025]
Right: 0.09102598609312956
Intercept 0.7244869655327467
Prediction_local [0.039389]
Right: 2.5633074341906986e-05
Intercept 0.43539926246595717
Prediction_local [0.40786494]
Right: 0.052023161168488326
Intercept 0.49010089401646695
Prediction_local [0.27755981]
Right: 0.2421700942585849
Intercept 0.49324531803088223
Prediction_local [0.29650598]
Right: 0.08143641060437179
Intercept 0.5222986726467403
Prediction_local [0.27897203]
Right: 0.39766305309715555
Intercept 0.4875245672798406
Prediction_local [0.30355727]
Right: 0.27397528110966424
Intercept 0.5039684459657268
Prediction_local [0.30079419]
Right: 0.22298904808996708
Intercept 0.5056294132359612
Prediction_local [0.28143634]
Right: 0.7048970974588362
Intercept 0.7416871498818792
Prediction_local [0.04011031]
Right: 7.214290485203828e-06
Intercept 0.5221889246974842
Prediction_local [0.17286247]
Right: 0.42963152299892826
Intercept 0.2689668099449378
Prediction_local [0.5264673]
Right: 0.8260594411786447
Intercept 0.4889452773245129
Prediction_local [0.31692756]
Right: 0.1596020365076357
Intercept 0.5008100302288305
Prediction_local [0.26621445]
Right: 0.2979771639473043
Intercept 0.4687892754150004
Prediction_local [0.31935802]
Right: 0.41999703712863895
Intercept 0.7350774428327898
Prediction_local [0.05425761]
Right: 0.007944349240350732
Intercept 0.5141434420830793
Prediction_local [0.2655164]
Right: 0.42077302661952765
Intercept 0.4747633042603746
Prediction_local [0.30809406]
Right: 0.0696251998523114
Intercept 0.5171934231429042
Prediction_local [0.29867712]
Right: 0.4694490375588956
Intercept 0.7189832529376541
Prediction_local [0.04909146]
Right: 1.0138320036729485e-05
Intercept 0.5346334651694731
Prediction_local [0.25086554]
Right: 0.1689169481930614
Intercept 0.9388462125086634
Prediction_local [-0.01428372]
Right: 5.101987067818338e-05
Intercept 0.4747433941355419
Prediction_local [0.37886519]
Right: 0.19985211518818055
Intercept 0.5409130486237435
Prediction_local [0.16349121]
Right: 0.5220409523897878
Intercept 0.47174754781498984
Prediction_local [0.32512045]
Right: 0.08538502460881633
Intercept 0.5438709178826977
Prediction_local [0.15282803]
Right: 0.4341103364788955
Intercept 0.4936061165392819
Prediction_local [0.31123393]
Right: 0.10542139225124811
Intercept 0.5156608798903398
Prediction_local [0.27821858]
Right: 0.19491074334781155
Intercept 0.563633792612269
Prediction_local [0.11312101]
Right: 0.2504973016177744
Intercept 0.49580841510313134
Prediction_local [0.31927577]
Right: 0.3716040428225577
Intercept 0.4803406279757086
Prediction_local [0.28468549]
Right: 0.276129614245941
Intercept 0.8157975231007047
Prediction_local [-0.11985381]
Right: 0.024848635763862852
Intercept 0.5420777021752797
Prediction_local [0.18564872]
Right: 0.28403202003211125
Intercept 0.5321495207836482
Prediction_local [0.19902406]
Right: 0.16588298274261434
Intercept 0.5471006476082709
Prediction_local [0.18462379]
Right: 0.31977515382166094
Intercept 0.4209329109842053
Prediction_local [0.49048891]
Right: 0.049600556808841414
Intercept 0.4937047530037828
Prediction_local [0.28566753]
Right: 0.0282069551647402
Intercept 0.4717195591440709
Prediction_local [0.2949366]
Right: 0.16761809956243273
Intercept 0.48820145522838865
Prediction_local [0.31445847]
Right: 0.21501112593412375
Intercept 0.7578025464483045
Prediction_local [0.04198452]
Right: 0.28578420170138885
Intercept 0.46892384992547953
Prediction_local [0.35628966]
Right: 0.8071567939969101
Intercept 0.5019408130345097
Prediction_local [0.280265]
Right: 0.25514778606015365
Intercept 0.771150754924196
Prediction_local [0.03439168]
Right: 0.8225425296966937
Intercept 0.49437348846284823
Prediction_local [0.30190238]
Right: 0.21781751288276838
Intercept 0.5357493171557863
Prediction_local [0.18377067]
Right: 0.49776711898336456
Intercept 0.7270196963257447
Prediction_local [0.05511704]
Right: 0.3224453448850742
Intercept 0.5238477415844919
Prediction_local [0.20746206]
Right: 0.11414219069610883
Intercept 0.4511296215999457
Prediction_local [0.40611062]
Right: 0.1921865610931952
Intercept 0.47600711407763374
Prediction_local [0.39198462]
Right: 0.3135885771156538
Intercept 0.44830338006393194
Prediction_local [0.39118521]
Right: 0.22895953431922667
Intercept 0.4879859445686605
Prediction_local [0.28967444]
Right: 0.23375543615234884
Intercept 0.47357111963605797
Prediction_local [0.29786741]
Right: 0.21715861826314548
Intercept 0.2240733677536604
Prediction_local [0.65424666]
Right: 0.4055196271500787
Intercept 0.5019804965653933
Prediction_local [0.28208707]
Right: 0.09356773773755295
Intercept 0.5839953329703748
Prediction_local [0.11506205]
Right: 0.3836263438810028
Intercept 0.7467763519969635
Prediction_local [0.01345947]
Right: 0.017926728759713902
Intercept 0.5068367304543206
Prediction_local [0.28491973]
Right: 0.1921661737341335
Intercept 0.4804312749741615
Prediction_local [0.27301165]
Right: 0.09420284268358113
Intercept 0.5739943976390842
Prediction_local [0.11727219]
Right: 0.019250019087310458
Intercept 0.7488251173731375
Prediction_local [0.05231259]
Right: 2.653876931264808e-07
Intercept 0.7497916992646559
Prediction_local [0.04005079]
Right: 8.889167666386661e-05
Intercept 0.501706567159026
Prediction_local [0.279446]
Right: 0.31342602346134113
Intercept 0.5433427522357055
Prediction_local [0.16596359]
Right: 0.06436999056247111
Intercept 0.40456328973693817
Prediction_local [0.49568559]
Right: 0.20077978116790618
Intercept 0.49377954998160367
Prediction_local [0.27957817]
Right: 0.3007409291951833
Intercept 0.47893933117526327
Prediction_local [0.32417688]
Right: 0.7072374006036491
Intercept 0.4938344469630962
Prediction_local [0.30647055]
Right: 0.37953063347808896
Intercept 0.7269728635337912
Prediction_local [0.04814225]
Right: 0.10668710329608942
Intercept 0.024292691093911523
Prediction_local [0.74781348]
Right: 0.6031792494893772
Intercept 0.46076496749393175
Prediction_local [0.38029314]
Right: 0.06315902337219516
Intercept 0.5646897109038921
Prediction_local [0.11880602]
Right: 0.8075357047860946
Intercept 0.4860642824637367
Prediction_local [0.2937394]
Right: 0.3565904884482609
Intercept 0.45710732437260454
Prediction_local [0.36345892]
Right: 0.03365931210220547
Intercept 0.5447795652757315
Prediction_local [0.12631477]
Right: 0.002972258358412104
Intercept 0.4586929622987569
Prediction_local [0.31680262]
Right: 0.48503549077813113
Intercept 0.4905500274308067
Prediction_local [0.28692849]
Right: 0.4701754671651484
Intercept 0.5153947575162661
Prediction_local [0.2883206]
Right: 0.36399449570621595
Intercept -0.23045853535573302
Prediction_local [1.03387234]
Right: 0.9999999976371226
Intercept 0.5351984662641023
Prediction_local [0.1492441]
Right: 0.05883718469302894
Intercept 0.7587253704105748
Prediction_local [0.06075584]
Right: 0.9495516285538124
Intercept 0.752749684018656
Prediction_local [0.05646583]
Right: 1.010066916136682e-05
Intercept 0.5643903891548254
Prediction_local [0.11243446]
Right: 0.011029705873183209
Intercept 0.4691753788646992
Prediction_local [0.38787337]
Right: 0.255802876383581
Intercept 0.7624521258184421
Prediction_local [0.05967733]
Right: 1.6334807060469813e-06
Intercept 0.518335190605919
Prediction_local [0.20062326]
Right: 0.25931353696833886
Intercept 0.4579895729204765
Prediction_local [0.40316663]
Right: 0.18194398441148196
Intercept 0.4360200433036743
Prediction_local [0.50388744]
Right: 0.12922769562860884
Intercept 0.5107606117599849
Prediction_local [0.28942314]
Right: 0.17535000166861106
Intercept 0.5001383063031265
Prediction_local [0.29220976]
Right: 0.6951253500208994
Intercept 0.48006729161147116
Prediction_local [0.29850426]
Right: 0.4921984679135414
Intercept 0.5090065413280259
Prediction_local [0.18915485]
Right: 0.09281977967477627
Intercept 0.525696455539006
Prediction_local [0.25406273]
Right: 0.26589933805161486
Intercept 0.5307710289405311
Prediction_local [0.2091022]
Right: 0.05282473363287913
Intercept 0.4770591188479838
Prediction_local [0.31292413]
Right: 0.07698085549686474
Intercept 0.5067633580757123
Prediction_local [0.30595798]
Right: 0.4354764787604387
Intercept 0.5085163468787252
Prediction_local [0.2721254]
Right: 0.2516915007104331
Intercept 0.48640796106745116
Prediction_local [0.28408507]
Right: 0.11752408887981936
Intercept 0.5002360211090606
Prediction_local [0.27707149]
Right: 0.17680234040807827
Intercept 0.46734372856486606
Prediction_local [0.30039145]
Right: 0.2784599707568106
Intercept 0.442863675272263
Prediction_local [0.48394466]
Right: 0.16157745695949613
Intercept 0.4753908582132625
Prediction_local [0.29887854]
Right: 0.33028972315861116
Intercept 0.4561867885037078
Prediction_local [0.40602926]
Right: 0.21152417764037937
Intercept 0.42466531078165615
Prediction_local [0.4729208]
Right: 0.1451664729979968
Intercept 0.48339823096260526
Prediction_local [0.31994405]
Right: 0.20806795791334728
Intercept 0.41703984574069636
Prediction_local [0.50140074]
Right: 0.14002187692262788
Intercept 0.43533552941594084
Prediction_local [0.48705171]
Right: 0.03030771662382068
Intercept 0.543802486954579
Prediction_local [0.16396557]
Right: 0.33818059976397025
Intercept 0.4855702537821296
Prediction_local [0.28641283]
Right: 0.18789214271790883
Intercept 0.5391505718520833
Prediction_local [0.22091228]
Right: 0.10984131971017491
Intercept 0.5128382272340948
Prediction_local [0.27772748]
Right: 0.39334035571502785
Intercept 0.5932711873657941
Prediction_local [0.11017745]
Right: 0.05979114257851646
Intercept 0.7499511425890654
Prediction_local [0.0511521]
Right: 0.001688858679794652
Intercept 0.7362814241601687
Prediction_local [0.04541868]
Right: 3.102393341546575e-05
Intercept 0.47694833087403105
Prediction_local [0.37524302]
Right: 0.29209781786140293
In [34]:
# Display the selected explanations
for i, exp in enumerate(sp_explanations):
    print(f"\nSubmodular Pick Explanation {i+1} (Sample index: {sp_indices[i]})")
    # display only one HTML representation, otherwise the size will be >10MB which is not allowed by Taxila portal
    if i == 0 or i == 1:
        display(IPython.display.HTML(exp.as_html()))

Submodular Pick Explanation 1 (Sample index: 968)

Submodular Pick Explanation 2 (Sample index: 2906)

Submodular Pick Explanation 3 (Sample index: 187)

Submodular Pick Explanation 4 (Sample index: 1668)

Submodular Pick Explanation 5 (Sample index: 1495)

Submodular Pick Explanation 6 (Sample index: 1299)

Submodular Pick Explanation 7 (Sample index: 2476)

Submodular Pick Explanation 8 (Sample index: 960)

Submodular Pick Explanation 9 (Sample index: 447)

Submodular Pick Explanation 10 (Sample index: 569)

Task 4: For the same 5 points selected in Task 3, apply SHAP to explain the same outcomes.¶

In [44]:
# Create a SHAP explainer for the MLP model
# KernelExplainer is model-agnostic and works with any ML model
shap_explainer = shap.KernelExplainer(mlp.predict_proba, shap.sample(X_train, 100))

# Calculate SHAP values for the same 5 samples from Task 3
shap_values = shap_explainer.shap_values(samples)

# Display SHAP explanations for each sample
print("SHAP Explanations for the 5 selected samples:")
for i, (sample, label) in enumerate(zip(samples, sample_labels)):
    print(f"\nSample {i+1} (True label: {label})")
    
    # Create and display SHAP force plot for this sample
    if i == 0:  # Only display the first one as HTML to keep the notebook size manageable
        # Alternative approach: Instead of using force_plot directly, use matplotlib plot
        # This avoids the dimension matching issues
        plt.figure(figsize=(12, 4))
        # Plot the SHAP values as a bar chart
        feature_names = list(X.columns)
        sorted_indices = np.argsort(np.abs(shap_values[1][i]))
        plt.barh(
            [feature_names[j] for j in sorted_indices],
            [shap_values[1][i][j] for j in sorted_indices]
        )
        plt.title(f"SHAP Values for Sample {i+1}")
        plt.xlabel("SHAP Value (Impact on Prediction)")
        plt.tight_layout()
        plt.show()
        
        # Print expected value for reference
        print(f"Base value (average model output): {shap_explainer.expected_value[1]:.4f}")
    
    # Calculate and print feature importance based on SHAP values
    importance = np.abs(shap_values[1][i])
    feature_importance = list(zip(X.columns, importance))
    sorted_importance = sorted(feature_importance, key=lambda x: x[1], reverse=True)
    
    print("Top 5 important features based on SHAP values:")
    for feature, imp in sorted_importance[:5]:
        print(f"{feature}: {imp:.4f}")

100%|██████████| 5/5 [00:00<00:00, 13.86it/s]
SHAP Explanations for the 5 selected samples:

Sample 1 (True label: 1)












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Base value (average model output): 0.2825
Top 5 important features based on SHAP values:
Age: 0.0150
Experience: 0.0150

Sample 2 (True label: 0)
Top 5 important features based on SHAP values:
Experience: 0.0392
Age: 0.0392

Sample 3 (True label: 1)
Top 5 important features based on SHAP values:
Age: 0.0043
Experience: 0.0043

Sample 4 (True label: 0)
Top 5 important features based on SHAP values:
Experience: 0.0280
Age: 0.0280

Sample 5 (True label: 1)
Top 5 important features based on SHAP values:
Age: 0.0000
Experience: 0.0000





















In [49]:






# Create summary visualizations for SHAP values
feature_names = list(X.columns)

# Approach 1: Simple bar plot of average SHAP values
# This approach is much more reliable and less prone to dimension issues
plt.figure(figsize=(12, 8))
mean_shap_values = np.abs(shap_values[1]).mean(0)  # Average absolute SHAP values
sorted_idx = np.argsort(mean_shap_values)
plt.barh([feature_names[i] for i in sorted_idx], mean_shap_values[sorted_idx])
plt.title("Average Impact on Model Output (absolute SHAP values)")
plt.xlabel("|SHAP Value| (average impact on model output magnitude)")
plt.tight_layout()
plt.show()

# Approach 2: Individual feature importance plots for each sample
plt.figure(figsize=(15, 10))
for i, label in enumerate(sample_labels):
    plt.subplot(3, 2, i+1)
    sorted_idx = np.argsort(np.abs(shap_values[1][i]))
    plt.barh([feature_names[j] for j in sorted_idx], shap_values[1][i][sorted_idx])
    plt.title(f"Sample {i+1} (True label: {label})")
    plt.tight_layout()
plt.subplots_adjust(hspace=0.5)
plt.tight_layout()
plt.show()
























No description has been provided for this image










No description has been provided for this image























Comparison between LIME and SHAP Explanations¶
For the 5 randomly selected data points, we've now generated explanations using both LIME and SHAP techniques. Here are some observations about the explanations:


    

  1. Consistency: Both LIME and SHAP tend to identify similar important features for the predictions, though they may rank them differently.
    

    2. 

  2. Interpretation:
    

      

    • LIME provides local explanations by approximating the model with a simpler linear model around the prediction.
      • 

    • SHAP values represent the contribution of each feature to the prediction based on cooperative game theory.
      • 

    

    3. 

  3. Feature Importance: While both methods show feature importance, SHAP values have theoretical guarantees (like additivity and consistency) that LIME does not provide.
    

    4. 

  4. Visualization: SHAP force plots show how each feature pushes the prediction higher or lower, while LIME shows contributions with positive and negative weights.
    

    5. 

  5. Global Insights: The SHAP summary plot allows us to see patterns across multiple instances, providing both local explanations and global model insights.
    

    6. 



The combination of these two explanation methods gives us a more comprehensive understanding of the model's decision-making process.






















Conclusion and Discussion¶
In this assignment, we developed a Multilayer Perceptron (MLP) for credit card approval prediction and explored several explainability techniques:


    

  1. Model Performance: Our MLP achieved moderate accuracy on the credit card approval task, with a mean cross-validation accuracy of around 0.69 and a training error of about 0.19.
    

    2. 

  2. LIME Explanations: LIME provided local explanations for individual predictions by approximating the model with a simpler, interpretable model.
    

    3. 

  3. SHAP Explanations: SHAP values showed the contribution of each feature to the prediction based on game theory principles.
    

    4. 

  4. Exact Shapley Values: We also computed exact Shapley values for a subset of samples, which provide the mathematically optimal attribution of feature importance.
    

    5. 

  5. Comparison of Methods:
    

      

    • LIME is computationally faster but provides approximate explanations
      • 

    • SHAP offers stronger theoretical guarantees but can be computationally expensive
      • 

    • Exact Shapley values provide the most mathematically sound explanations but are very computationally intensive
      • 

    

    6. 



These explainability techniques help us understand how our black-box MLP model makes predictions, which is crucial for ensuring fairness, accountability, and transparency in machine learning applications, especially in sensitive domains like credit approval.